Technique for designing acoustic microwave filters using lcr-based resonator models

ABSTRACT

A method of designing an acoustic microwave filter in accordance with frequency response requirements comprises generating a modeled filter circuit design having a plurality of circuit elements comprising an acoustic resonant element defined by an electrical circuit model that comprises a parallel static branch, a parallel motional branch, and one or both of a parallel Bragg Band branch that models an upper Bragg Band discontinuity and a parallel bulk mode function that models an acoustic bulk mode loss. The method further comprises optimizing the modeled filter circuit design to generate an optimized filter circuit design, comparing a frequency response of the optimized filter circuit design to the frequency response requirements, and constructing the acoustic microwave filter from the optimized filter circuit design based on the comparison.

RELATED APPLICATION DATA

The present application is continuation of U.S. patent application Ser.No. 14/941,477, filed Nov. 13, 2015, which is expressly incorporated byreference into the present application in its entirety.

FIELD OF THE INVENTION

The present inventions generally relate to microwave filters, and moreparticularly, to acoustic microwave filters designed for narrow-bandapplications.

BACKGROUND OF THE INVENTION

Electrical filters have long been used in the processing of electricalsignals. In particular, such electrical filters are used to selectdesired electrical signal frequencies from an input signal by passingthe desired signal frequencies, while blocking or attenuating otherundesirable electrical signal frequencies. Filters may be classified insome general categories that include low-pass filters, high-passfilters, band-pass filters, and band-stop filters, indicative of thetype of frequencies that are selectively passed by the filter. Further,filters can be classified by type, such as Butterworth, Chebyshev,Inverse Chebyshev, and Elliptic, indicative of the type of bandshapefrequency response (frequency cutoff characteristics) the filterprovides relative to the ideal frequency response.

The type of filter used often depends upon the intended use. Incommunications applications, band pass and band stop filters areconventionally used in cellular base stations, cell phone handsets, andother telecommunications equipment to filter out or block RF signals inall but one or more predefined bands. Of most particular importance isthe frequency range from approximately 500-3,500 MHz. In the UnitedStates, there are a number of standard bands used for cellularcommunications. These include Band 2 (˜1800-1900 MHz), Band 4(˜1700-2100 MHz), Band 5 (˜800-900 MHz), Band 13 (˜700-800 MHz), andBand 17 (˜700-800 MHz); with other bands emerging.

Microwave filters are generally built using two circuit building blocks:a plurality of resonators, which store energy very efficiently at aresonant frequency (which may be a fundamental resonant frequency f₀ orany one of a variety of higher order resonant frequencies f₁-f_(n)); andcouplings, which couple electromagnetic energy between the resonators toform multiple reflection zeros providing a broader spectral response.For example, a four-resonator filter may include four reflection zeros.The strength of a given coupling is determined by its reactance (i.e.,inductance and/or capacitance). The relative strengths of the couplingsdetermine the filter shape, and the topology of the couplings determineswhether the filter performs a band-pass or a band-stop function. Theresonant frequency f₀ is largely determined by the inductance andcapacitance of the respective resonator. For conventional filterdesigns, the frequency at which the filter is active is determined bythe resonant frequencies of the resonators that make up the filter. Eachresonator must have very low internal resistance to enable the responseof the filter to be sharp and highly selective for the reasons discussedabove. This requirement for low resistance tends to drive the size andcost of the resonators for a given technology.

The duplexer, a specialized kind of filter is a key component in thefront-end of mobile devices. Modern mobile communications devicestransmit and receive at the same time (using LTE, WCDMA or CDMA) and usethe same antenna. The duplexer separates the transmit signal, which canbe up to 0.5 Watt power, from the receive signal, which can be as low asa pico-Watt. The transmit and receive signals are modulated on carriersat different frequencies allowing the duplexer to select them. Theduplexer must provide the frequency selection, isolation and lowinsertion loss in a very small size often only about two millimeterssquare.

The front-end receive filter preferably takes the form of a sharplydefined band-pass filter to eliminate various adverse effects resultingfrom strong interfering signals at frequencies near the desired receivedsignal frequency. Because of the location of the front-end receiverfilter at the antenna input, the insertion loss must be very low so asto not degrade the noise figure. In most filter technologies, achievinga low insertion loss requires a corresponding compromise in filtersteepness or selectivity.

In practice, most filters for cell phone handsets are constructed usingacoustic resonator technology, such as surface acoustic wave (SAW), bulkacoustic wave (BAW), and film bulk acoustic resonator (FBAR)technologies. The acoustic resonator has two resonances closely spacedin frequency called the “resonance” frequency and the “anti-resonance”frequency (see K. S. Van Dyke, Piezo-Electric Resonator and itsEquivalent Network Proc. IRE, Vol. 16, 1928, pp. 742-764). Such acousticresonators have the advantages of low insertion loss (on the order of 1dB at the center frequency), compact size, and low cost compared toequivalent inductor/capacitor resonators. For this reason, acousticresonator implementations are often used for microwave filteringapplications in the front-end receive filter of mobile devices. Acousticresonators are typically arranged in a ladder topology (alternatingseries and shunt resonators) in order to create band pass filters.Acoustic ladder filters have been very successful for handsetapplications, with more than a billion units currently sold each year.

The design of modern microwave filters with acoustic resonators requiresdetailed models to predict the frequency response of the filter,including the upper edge of the Bragg Band and the bulk acoustic loss.In particular, a typical acoustic resonator has a plurality ofinterdigitized fingers (e.g., 80-100 fingers) that reflect acousticwaves back and forth between the fingers. The bulk loss is an acousticmode into which some of the acoustic energy is transferred when thefingers of the acoustic resonator are excited. The Bragg Band is thefrequency band over which the acoustic reflections between the fingersadd in phase to create the resonance. A discontinuity feature in thefrequency response occurs at the upper edge of the Bragg Band, i.e., thehighest frequency at which the acoustic reflections add in phase.Because the performance of the filter may be compromised if thisdiscontinuity feature falls within the passband, it is important todetermine the upper edge of the Bragg Band to ensure that thediscontinuity feature falls well outside of the passband of the filter.

A typical acoustic filter design process requires the use of a trainingmask that consists of a collection of resonators that span the necessaryresonator parameters, including, but not limited to, the number offinger pairs, aperture size, pitch, and transducer metal thickness. Thistraining mask must be fabricated, which can take anywhere from a coupleweeks to a month. The frequency responses of the training mask, whichwill include bulk loss and the discontinuity feature corresponding tothe upper edge of the Bragg Band, are then measured, which are then usedto create Coupling of Modes (COM) models to be used for the simulation,and ultimately the design, of the acoustic filters. Any errors in thetraining mask measurements can lead to less accurate COM models, whichwill result in poor correlations between the simulations and filtermeasurements.

There, thus, remains a need to provide a more efficient and accuratetechnique for modeling acoustic microwave filters.

SUMMARY OF THE INVENTION

In accordance with the present inventions, a method of designing anacoustic microwave filter in accordance with frequency responserequirements is provided. The frequency response requirements maycomprise one or more of a frequency dependent return loss, insertionloss, rejection, and linearity. The frequency response requirements maycomprise a pass band, e.g., one in the 300 MHz to 300 GHz range,specifically in the 300 MHz to 10.0 GHz range, and more specifically inthe 500-3500 MHz range.

The method comprises generating a modeled filter circuit design having aplurality of circuit elements comprising an acoustic resonant elementdefined by an electrical circuit model. The acoustic resonant elementmay, e.g., be one of a surface acoustic wave (SAW) resonator, a bulkacoustic wave (BAW) resonator, a film bulk acoustic resonator (FBAR),and a microelectromechanical system (MEMS) resonator. The modeled filtercircuit design may have, e.g., an Nth order ladder topology.

The resonator electrical circuit model comprises a parallel staticbranch, a parallel motional branch, and one or both of a parallel BraggBand branch that models an upper Bragg Band discontinuity and a parallelbulk mode function that models an acoustic bulk mode loss. In oneembodiment, the parallel static branch comprises a static capacitance,and the parallel motional branch comprises a motional inductance and amotional capacitance. The electrical circuit model may optionallycomprise at least one resistor that models an electrical loss of theacoustic resonant element. The Bragg Band branch may comprise a seriesLRC circuit, and/or the bulk mode function may be a hyperbolic tangentfunction, e.g., in accordance with

${Y = {h*\left( {1 - \frac{1}{10^{({\frac{freq}{w{({10^{6} - {Fb}})}} + 1})}}} \right)}},$

where Y is the bulk mode loss in dB; h is a scaling factor used to matchthe loss of the bulk mode; F_(b) is a frequency in Hz used to match theonset frequency of the bulk mode, w is a scaling factor used to matchthe steepness of the onset of the bulk mode, and freq is the frequencyof the input signal.

The method further comprises optimizing the modeled filter circuitdesign to generate an optimized filter circuit design, comparing afrequency response of the optimized filter circuit design to thefrequency response requirements, and constructing the acoustic microwavefilter from the optimized filter circuit design based on the comparison.

In one embodiment, the modeled filter circuit design is generated bydefining a physical model of the acoustic resonant element (e.g., byselecting a parameter consisting of at least one of a material, one ormore of a number of finger pairs, aperture size, mark-to-pitch ratio,and transducer metal thickness), simulating the physical model of theacoustic resonant element to generate a first frequency response (e.g.,by using a Finite Element Model (FEM)), simulating the electricalcircuit model of the acoustic resonant element to generate a secondfrequency response, comparing the first and second frequency responses,and modifying at least one parameter in the electrical circuit modelbased on the comparison prior to the optimization of the modeledelectrical filter circuit design.

Defining the physical model of the acoustic resonant element maycomprise, e.g., defining a first set of resonator characteristics forthe acoustic resonant element, simulating the physical model of theacoustic resonant element to generate a second set of resonatorcharacteristics, comparing the first and second sets of resonatorcharacteristics, and modifying at least one parameter of the physicalmodel of the acoustic resonant element based on the comparison. Each ofthe first and second sets of resonator characteristics may comprise,e.g., one or both of a resonant frequency and a static capacitance. Inthis case, optimizing the modeled filter circuit design may compriseoptimizing the resonant frequency and/or a static capacitance.

Comparing the frequency response of the optimized filter circuit designto the frequency response requirements may comprise, e.g., simulatingthe electrical circuit model of the acoustic resonant element of theoptimized filter circuit design to generate a third set of resonatorcharacteristics, simulating the physical model of the acoustic resonantelement to generate a fourth set of resonator characteristics, comparingthe third set of resonator characteristics to the fourth set ofresonator characteristics, modifying the parameter of the physical modelof the acoustic resonator based on the comparison, simulating thephysical model of the acoustic resonant element with the modifiedparameter to generate another frequency response, replacing theelectrical circuit model of the acoustic resonant element in theoptimized filter circuit design with the other frequency response tocreate a modified optimized filter circuit design, and simulating themodified optimized filter circuit design to create the frequencyresponse. Each of the third and fourth sets of resonator characteristicsmay comprise one or both of a resonant frequency and a staticcapacitance.

Other and further aspects and features of the invention will be evidentfrom reading the following detailed description of the preferredembodiments, which are intended to illustrate, not limit, the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate the design and utility of preferred embodimentsof the present invention, in which similar elements are referred to bycommon reference numerals. In order to better appreciate how theabove-recited and other advantages and objects of the present inventionsare obtained, a more particular description of the present inventionsbriefly described above will be rendered by reference to specificembodiments thereof, which are illustrated in the accompanying drawings.

Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 is a block diagram of a wireless telecommunications system;

FIG. 2 is a flow diagram of a technique used to design a microwaveacoustic filter for use in the wireless telecommunications system ofFIG. 3;

FIG. 3 is a schematic diagram of a microwave acoustic filter arranged inan Nth order ladder topology;

FIG. 4 is a schematic diagram illustrating the transformation of anacoustic resonator of the acoustic filter of FIG. 3 into an equivalentButterworth-Van Dyke (BVD) model;

FIG. 5a is a schematic diagram illustrating one equivalent modifiedButterworth-Van Dyke (MBVD) model into which the acoustic resonators ofthe acoustic filter of FIG. 3 can be transformed;

FIG. 5b is a schematic diagram illustrating another equivalent modifiedButterworth-Van Dyke (MBVD) model into which the acoustic resonators ofthe acoustic filter of FIG. 3 can be transformed;

FIG. 5c is a schematic diagram illustrating still another equivalentmodified Butterworth-Van Dyke (MBVD) model into which the acousticresonators of the acoustic filter of FIG. 3 can be transformed;

FIG. 5d is a schematic diagram illustrating yet another equivalentmodified Butterworth-Van Dyke (MBVD) model into which the acousticresonators of the acoustic filter of FIG. 3 can be transformed;

FIG. 6a is a measured s-parameter frequency response of an actualacoustic resonator and a simulated s-parameter frequency response of theequivalent MBVD model of FIG. 5a plotted against each other on a SmithChart;

FIG. 6b is a measured y-parameter frequency response of an actualacoustic resonator and a simulated y-parameter frequency response of theequivalent MBVD model of FIG. 5a plotted against each other from belowthe resonant frequency to above the upper Bragg Band frequency;

FIG. 6c is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5aplotted against each other from below the resonant frequency to abovethe resonant frequency;

FIG. 6d is a measured real portion of a z-parameter frequency responseof an actual acoustic resonator and a simulated real portion of az-parameter frequency response of the equivalent MBVD model of FIG. 5aplotted against each other from below the anti-resonant frequency toabove the anti-resonant frequency;

FIG. 6e is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5aplotted against each other from above the resonant frequency to abovethe upper Bragg Band frequency;

FIG. 6f is a measured real portion of a s-parameter frequency responseof an actual acoustic resonator and a simulated real portion of as-parameter frequency response of the equivalent MBVD model of FIG. 5aplotted against each other from below the upper Bragg Band frequency toabove the upper Bragg Band frequency;

FIG. 7a is a measured s-parameter frequency response of an actualacoustic resonator and a simulated s-parameter frequency response of theequivalent MBVD model of FIG. 5b plotted against each other on a SmithChart;

FIG. 7b is a measured y-parameter frequency response of an actualacoustic resonator and a simulated y-parameter frequency response of theequivalent MBVD model of FIG. 5b plotted against each other from belowthe resonant frequency to above the upper Bragg Band frequency;

FIG. 7c is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5bplotted against each other from below the resonant frequency to abovethe resonant frequency;

FIG. 7d is a measured real portion of a z-parameter frequency responseof an actual acoustic resonator and a simulated real portion of az-parameter frequency response of the equivalent MBVD model of FIG. 5bplotted against each other from below the anti-resonant frequency toabove the anti-resonant frequency;

FIG. 7e is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5bplotted against each other from above the resonant frequency to abovethe upper Bragg Band frequency;

FIG. 7f is a measured real portion of a s-parameter frequency responseof an actual acoustic resonator and a simulated real portion of as-parameter frequency response of the equivalent MBVD model of FIG. 5bplotted against each other from below the upper Bragg Band frequency toabove the upper Bragg Band frequency;

FIG. 8a is a measured s-parameter frequency response of an actualacoustic resonator and a simulated s-parameter frequency response of theequivalent MBVD model of FIG. 5c plotted against each other on a SmithChart;

FIG. 8b is a measured y-parameter frequency response of an actualacoustic resonator and a simulated y-parameter frequency response of theequivalent MBVD model of FIG. 5c plotted against each other from belowthe resonant frequency to above the upper Bragg Band frequency;

FIG. 8c is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5cplotted against each other from below the resonant frequency to abovethe resonant frequency;

FIG. 8d is a measured real portion of a z-parameter frequency responseof an actual acoustic resonator and a simulated real portion of az-parameter frequency response of the equivalent MBVD model of FIG. 5cplotted against each other from below the anti-resonant frequency toabove the anti-resonant frequency;

FIG. 8e is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5cplotted against each other from above the resonant frequency to abovethe upper Bragg Band frequency;

FIG. 8f is a measured real portion of a s-parameter frequency responseof an actual acoustic resonator and a simulated real portion of as-parameter frequency response of the equivalent MBVD model of FIG. 5cplotted against each other from below the upper Bragg Band frequency toabove the upper Bragg Band frequency;

FIG. 9a is a measured s-parameter frequency response of an actualacoustic resonator and a simulated s-parameter frequency response of theequivalent MBVD model of FIG. 5d plotted against each other on a SmithChart;

FIG. 9b is a measured y-parameter frequency response of an actualacoustic resonator and a simulated y-parameter frequency response of theequivalent MBVD model of FIG. 5d plotted against each other from belowthe resonant frequency to above the upper Bragg Band frequency;

FIG. 9c is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5dplotted against each other from below the resonant frequency to abovethe resonant frequency;

FIG. 9d is a measured real portion of a z-parameter frequency responseof an actual acoustic resonator and a simulated real portion of az-parameter frequency response of the equivalent MBVD model of FIG. 5dplotted against each other from below the anti-resonant frequency toabove the anti-resonant frequency;

FIG. 9e is a measured real portion of a y-parameter frequency responseof an actual acoustic resonator and a simulated real portion of ay-parameter frequency response of the equivalent MBVD model of FIG. 5dplotted against each other from above the resonant frequency to abovethe upper Bragg Band frequency; and

FIG. 9f is a measured real portion of a s-parameter frequency responseof an actual acoustic resonator and a simulated real portion of as-parameter frequency response of the equivalent MBVD model of FIG. 5dplotted against each other from below the upper Bragg Band frequency toabove the upper Bragg Band frequency.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure describes a technique for designing acoustic wave(AW) microwave filters (such as surface acoustic wave (SAW), bulkacoustic wave (BAW), film bulk acoustic resonator (FBAR),microelectromechanical system (MEMS) filters)). This technique can beapplied to AW microwave filters in the 300 MHz to 300 GHz frequencyrange, particularly in the 300 MHz to 10.0 GHz frequency range, and evenmore particularly in the 500 MHz to 3.5 GHz frequency range. Such AWmicrowave filters may be either fixed frequency and/or tunable filters(tunable in frequency and/or bandwidth and/or input impedance and/oroutput impedance), and may be used for single band or multiple bandpassand/or bandstop filtering. Such AW microwave filters are advantageous inapplications that have demanding electrical and/or environmentalperformance requirements and/or severe cost/size constraints, such asthose found in the radio frequency (RF) front ends of mobilecommunications devices, including cellphones, smartphones, laptopcomputers, tablet computers, etc. or the RF front ends of fixedcommunications devices, including M2M devices, wireless base stations,satellite communications systems, etc.

Example AW microwave filters described herein exhibit a frequencyresponse with a single passband, which is particularly useful intelecommunication system duplexers. For example, with reference to FIG.1, a telecommunications system 10 for use in a mobile communicationsdevice may include a transceiver 12 capable of transmitting andreceiving wireless signals, and a controller/processor 14 capable ofcontrolling the functions of the transceiver 12. The transceiver 12generally comprises a broadband antenna 16, a duplexer 18 having atransmit filter 24 and a receive filter 26, a transmitter 20 coupled tothe antenna 16 via the transmit filter 24 of the duplexer 18, and areceiver 22 coupled to the antenna 16 via the receive filter 26 of theduplexer 18.

The transmitter 20 includes an upconverter 28 configured for convertinga baseband signal provided by the controller/processor 14 to a radiofrequency (RF) signal, a variable gain amplifier (VGA) 30 configured foramplifying the RF signal, a bandpass filter 32 configured for outputtingthe RF signal at an operating frequency selected by thecontroller/processor 14, and a power amplifier 34 configured foramplifying the filtered RF signal, which is then provided to the antenna16 via the transmit filter 24 of the duplexer 18.

The receiver 22 includes a notch or stopband filter 36 configured forrejecting transmit signal interference from the RF signal input from theantenna 16 via the receiver filter 26, a low noise amplifier (LNA) 38configured for amplifying the RF signal from the stop band filter 36with a relatively low noise, a bandpass filter 40 configured foroutputting the amplified RF signal at a frequency selected by thecontroller/processor 14, and a downconverter 42 configured fordownconverting the RF signal to a baseband signal that is provided tothe controller/processor 14. Alternatively, the function of rejectingtransmit signal interference performed by the stop-band filter 36 caninstead be performed by the duplexer 18. Or, the power amplifier 34 ofthe transmitter 20 can be designed to reduce the transmit signalinterference.

It should be appreciated that the block diagram illustrated in FIG. 1 isfunctional in nature, and that several functions can be performed by oneelectronic component or one function can be performed by severalelectronic components. For example, the functions performed by the upconverter 28, VGA 30, bandpass filter 40, downconverter 42, andcontroller/processor 14 are oftentimes performed by a single transceiverchip. The function of the bandpass filter 32 can be performed by thepower amplifier 34 and the transmit filter 24 of the duplexer 18.

The exemplary technique described herein is used to design acousticmicrowave filters for the front-end of the telecommunications system 10,and in particular the transmit filter 24 of the duplexer 18, althoughthe same technique can be used to design acoustic microwave filters forthe receive filter 26 of the duplexer 18 and for other RF filters.

Referring now to FIG. 2, one exemplary technique 50 for designing an AWmicrowave filter will be described. First, the filter requirements,which comprise the frequency response requirements (including passband,return loss, insertion loss, rejection, linearity, noise figure, inputand output impedances, etc.), as well as size and cost requirements, andenvironmental requirements, such as operating temperature range,vibration, failure rate, etc., are define by the application of thefilter (step 52).

Next, the structural types of circuit elements to be used in the AWfilter are selected; for example, the structural type of resonator (SAW,BAW, FBAR, MEMS, etc.) and the types of inductor, capacitor, and switch,along with the materials to be used to fabricate these circuit elements,including the packaging and assembly techniques for fabricating thefilter, are selected (step 54). For example, SAW resonators may beselected, which may be fabricated by disposing interdigital transducers(IDTs) on a piezoelectric substrate, such as crystalline Quartz, LithiumNiobate (LiNbO₃), Lithium Tantalate (LiTaO₃) crystals or BAW (includingFBAR) resonators or MEMS resonators. In the particular example describedherein, the selection of circuit element types are SAW resonators andcapacitors constructed on a substrate composed of 42-degree XY-cutLiTaO3.

Then, a filter circuit topology is selected (step 56). In the embodimentillustrated in FIG. 3, the selected filter circuit topology is an Nthorder ladder topology (in this case, N=6 meaning the number ofresonators equals 6). The filter circuit topology 100 comprises a sourceresistance S, a load resistance L, three series (or in-line) acousticresonators Z_(S1)-Z_(S3), and three parallel (or in-shunt) acousticresonators Z_(P1)-Z_(P3). Nth order ladder topologies are described inU.S. Pat. Nos. 8,751,993 and 8,701,065 and U.S. patent application Ser.No. ______, entitled “Acoustic Wave Filter with Enhanced Rejection”(Attorney Docket No. RES-019), which are all expressly incorporatedherein by reference. Other filter circuit topologies, such as in-linenon-resonant-node, or in-line, or in-line with cross couplings, orin-line non-resonant node with cross couplings, etc., may be selected.

Then, a modeled filter circuit design having a plurality of circuitelements that includes at least one acoustic resonator is generated. Inparticular, an initial filter circuit design is synthesized usingsuitable filter circuit design techniques, resulting in the definitionof values for all of the circuit elements, including a first set ofresonator characteristics (e.g., a static capacitance, resonantfrequency, and gamma) for each of the acoustic resonators Z (step 58).Next, an initial physical model of each of the acoustic resonators Z isselected; for example, by selecting a material, one or more of a numberof finger pairs, aperture size, mark-to-pitch ratio, and/or transducermetal thickness (step 60); and each of the initial physical models ofthe acoustic resonators Z is iteratively simulated and modified untilthey match the initial filter circuit design, thereby generating themodeled filter circuit design. In particular, each of the initialphysical models of the acoustic resonators Z is simulated (e.g., using aFinite Element Model (FEM)) to determine frequency response and a secondset of resonator characteristics (e.g., the static capacitance andresonant frequency) for each of the physical acoustic models (step 62).

The second set of resonator characteristics of each of the physicalacoustic models is then respectively compared to the first set ofresonator characteristics of each of the acoustic resonators Z definedin step 58 (step 64). If the first and second sets of resonatorcharacteristics do not match each other (step 66), another physicalmodel of each of the acoustic resonators Z is selected; for example, bymodifying a material, one or more of a number of finger pairs, aperturesize, mark-to-pitch ratio, and/or transducer metal thickness (step 60),and steps 62-66 are repeated.

If the first and second sets of resonator characteristics do match eachother (step 66), an electrical circuit model, such as a modifiedButterworth-Van Dyke (MBVD) model, is selected for each of the acousticresonators Z_(P1)-Z_(P4) (step 68). The basic electrical circuit for aMBVD is the BVD model illustrated in FIG. 4. The BVD model 110 comprisesa parallel static branch 112 a and a parallel motional branch 112 b. Theparallel static branch 112 a includes a static capacitance C₀, and theparallel motional branch 112 b includes a motional capacitance C_(m) anda motional inductance L_(m). The motional capacitance C_(m) and motionalinductance L_(m) may result from the interactions of electrical andacoustical behavior, and thus, may be referred to as the motional arm ofthe BVD model 110. The static capacitance C₀ may result from thecapacitance of the structure, and thus, may be referred to as the static(non-motional) capacitance of the BVD model 110.

Various MBVD models can be derived from the basic BVD model 110 for usein modeling each of the acoustic resonators Z in the initial filtercircuit design 100.

For example, as illustrated in FIG. 5a , one MBVD model 110 a comprisesthe parallel static branch 112 a, the parallel motional branch 112 b,and a resistance R1 located in the parallel motional branch 112 b inseries with the motional capacitance C_(m) and a motional inductanceL_(m). The resistance R1 represents the loss caused from the electricalresistance of the acoustic resonator.

In another example illustrated in FIG. 5b , an MBVD model 110 bcomprises the parallel static branch 112 a, the parallel motional branch112 b, a resistance R2 located in a main branch 112 c, and a resistanceR3 located in parallel with the static capacitance C₀. The resistancesR2 and R3 represent the losses caused from the electrical resistance ofthe acoustic resonator.

In still another example illustrated in FIG. 5c , an MBVD model 110 ccomprises the parallel static branch 112 a, the parallel motional branch112 b, the resistances R2 and R3, and a parallel Bragg Band branch 112 dthat includes a resistance R_(b), an inductance L_(b), and a capacitanceC_(b). The Bragg Band branch 112 d models the upper Bragg Banddiscontinuity of the acoustic resonator.

In yet another example illustrated in FIG. 5d , an MBVD model 110 dcomprises the parallel static branch 112 a, the parallel motional branch112 b, the resistances R1 and R2, the parallel Bragg Band branch 112 d,and a parallel bulk mode function 112 e that models an acoustic bulkmode loss. The bulk bode function 112 e is a hyperbolic tangentfunction, which in the illustrated embodiment, is computed in accordancewith the following equation:

$\begin{matrix}{{Y = {h*\left( {1 - \frac{1}{10^{({\frac{freq}{w{({10^{6} - {Fb}})}} + 1})}}} \right)}},} & \lbrack 5\rbrack\end{matrix}$

where Y is the bulk mode loss in dB; h is a scaling factor used to matchthe loss of the bulk mode; F_(b) is a frequency in Hz used to match theonset frequency of the bulk mode, w is a scaling factor used to matchthe steepness of the onset of the bulk mode, and freq is the frequencyof the input signal.

A SAW resonator was fabricated and modeled using the differentelectrical circuit models 110 a-110 d created in accordance with theequations [1]-[3]. Various types of frequency responses of thefabricated acoustic resonator were measured and simulated with thedifferent electrical circuit models 110 a-110 d. As illustrated in FIGS.6-9, the resonant frequency 120, anti-resonant frequency 122, upperBragg Band frequency 124, and Bulk Mode range 126 of the frequencyresponses of the respective electrical circuit models 110 a-110 d can becompared to each other relative to the measured frequency responses ofthe fabricated acoustic resonator.

In particular, the measurement of the fabricated acoustic resonator andthe simulated MBVD models 110 a-110 d respectively yielded thes-parameter (S11 return loss) frequency responses plotted on a SmithChart over a frequency range from below the resonant frequency of theSAW resonator to above the upper Bragg Band of the SAW resonator (FIGS.6a, 7a, 8a, and 9a ); the y-parameter frequency responses plotted indecibels over a frequency range from below the resonant frequency of theSAW resonator to above the upper Bragg Band of the SAW resonator (FIGS.6b, 7b, 8b, and 9b ); the real part of the y-parameter frequencyresponses plotted in Siemens over a frequency range centered around theresonant frequency of the SAW resonator (FIGS. 6c, 7c, 8c, and 9c ); thereal part of the z-parameter frequency responses plotted in ohms over afrequency range centered around the anti-resonant frequency of the SAWresonator (FIGS. 6d, 7d, 8d, and 9d ); the real part of the y-parameterfrequency responses plotted in Siemens over a frequency range from abovethe resonant frequency of the SAW resonator to above the upper BraggBand of the SAW resonator (FIGS. 6e, 7e, 8e, and 9e ); and thes-parameter (S11 return loss) frequency responses plotted over afrequency range centered on the upper Bragg Band frequency of the SAWresonator (FIGS. 6f, 7f, 8f, and 9f ).

The single-component loss model of the electrical circuit model 110 a(i.e., resistor R1 in FIG. 5a ) does not exactly match the actualelectrical loss of the fabricated acoustic resonator, resulting insubstantial differences between the simulated frequency response andmeasured frequency response in terms of the resonant frequency 120 andanti-resonant frequency 122, as shown in the plots of FIGS. 6c and 6d .The absence of a Bragg band branch and bulk mode function in theelectrical circuit model 110 a results in even larger differencesbetween the simulated frequency response and measured frequency responsein terms of the upper Bragg Band frequency 124 and Bulk Mode range 126,as shown in the plots of FIGS. 6a, 6e , and 6 f.

In contrast, compared to the single-component loss model of theelectrical circuit model 110 a, the two-component loss model of theelectrical circuit model 110 b (i.e., resistors R2 and R3 in FIG. 5b )better matches the actual electrical loss of the fabricated acousticresonator, resulting in insubstantial differences between the simulatedfrequency response and measured frequency response in terms of theresonant frequency 120 and anti-resonant frequency 122, as shown in theplots of FIGS. 7c and 7d . However, like the electrical circuit model110 a, the absence of a Bragg band branch and bulk mode function in theelectrical circuit model 110 b results in large differences between thesimulated frequency response and measured frequency response in terms ofthe upper Bragg Band frequency 124 and Bulk Mode range 126, as shown inthe plots of FIGS. 7a, 7e , and 7 f.

Like the two-component loss model of the electrical circuit model 110 b,the two-component loss model of the electrical circuit model 110 c(i.e., resistors R2 and R3 in FIG. 5c ) matches the actual electricalloss of the fabricated acoustic resonator, resulting in insubstantialdifferences between the simulated frequency response and measuredfrequency response in terms of the resonant frequency 120 andanti-resonant frequency 122, as shown in the plots of FIGS. 8c and 8d .In contrast to the electrical circuit model 110 b, the additional BraggBand branch 112 d of the electrical circuit model 110 c (FIG. 5c )substantially matches the upper Bragg Band discontinuity of thefabricated acoustic resonator, resulting in insubstantial differencesbetween the simulated frequency response and measured frequency responsein terms of the upper Bragg band frequency 124, as shown in the plots ofFIGS. 8a and 8e . However, like the electrical circuit model 110 b, theabsence of a bulk mode function in the electrical circuit model 110 cresults in large differences between the simulated frequency responseand measured frequency response in terms of the Bulk Mode range 126, asshown in the plots of FIG. 8 f.

Like the two-component loss model of the electrical circuit model 110 c,the two-component loss model of the electrical circuit model 110 c(i.e., resistors R2 and R3 in FIG. 5d ) matches the actual electricalloss of the fabricated acoustic resonator, resulting in insubstantialdifferences between the simulated frequency response and measuredfrequency response in terms of the resonant frequency 120 andanti-resonant frequency 122, as shown in the plots of FIGS. 9c and 9d .Also like the electrical circuit model 110 c, the Bragg Band branch 112d of the electrical circuit model 110 d (FIG. 5d ) substantially matchesthe upper Bragg Band discontinuity of the fabricated acoustic resonator,resulting in insubstantial differences between the simulated frequencyresponse and measured frequency response in terms of the upper Braggband frequency 124, as shown in the plots of FIGS. 9a and 9e . Incontrast to the electrical circuit model 110 c, the additional Bulk Modefunction 112 e substantially matches the Bulk Mode loss of thefabricated acoustic resonator, resulting in insubstantial differencesbetween the simulated frequency response and measured frequency responsein terms of the Bulk Mode range 126, as shown in the plot of FIG. 8 f.

After the electrical circuit model (e.g., one of the MBVD models 110a-110 d) is selected for each of the acoustic resonators Z at step 68,the electrical circuit models are fitted to the physical acousticmodels, thereby generating the modeled filter circuit design; that is,the electrical circuit models are iteratively simulated and modifieduntil they respectively match the physical models of the acousticresonators Z. In particular, values for the circuit elements in each ofthe electrical circuit models are selected based on the values of thefirst set of resonator characteristics (e.g., static capacitance,resonant frequency, and gamma) selected for the initial filter circuitdesign in step 58 (step 70).

Notably, the circuit values of the selected MBVD model 110 are relatedby the following equations:

$\begin{matrix}{{\omega_{R} = \frac{1}{\sqrt{L_{m}C_{m}}}};} & \lbrack 1\rbrack \\{{\frac{\omega_{A}}{\omega_{R}} = \sqrt{1 + \frac{1}{\gamma}}},} & \lbrack 2\rbrack\end{matrix}$

where ω_(R) and ω_(A) may be the respective resonance and anti-resonancefrequencies for any given acoustic resonator, and gamma γ may depend ona material's property, which may be further defined by:

$\begin{matrix}{\frac{C_{0}}{C_{m}} = \gamma} & \lbrack 3\rbrack\end{matrix}$

Typical γ values may range from about 12 to about 18 for 42-degree X Ycut LiTaO₃. The frequency separation of an acoustic resonator means thedifference between its resonant frequency and its anti-resonantfrequency. The percentage separation of an acoustic wave resonator isthe percentage frequency separation between its resonant frequency andanti-resonant frequency, and can be computed, as follows:

$\begin{matrix}{{{percentage}\mspace{14mu} {separation}} = {\sqrt{1 + \left( \frac{1}{\gamma} \right)} - 1}} & \lbrack 4\rbrack\end{matrix}$

where γ is the ratio of the static to the motional capacitance of theresonator (equation [3]), as determined by the material properties ofthe piezoelectric material and modified by the geometry of the device.

It can be appreciated from equation [1] that the resonant frequency ofeach of the acoustic resonators will depend on the motional arm of theBVD model 110, whereas the filter characteristics (e.g., bandwidth) willbe strongly influenced by γ in equation [2]. The Quality factor (Q) foran acoustic resonator 110 may be an important figure of merit inacoustic filter design, relating to the loss of the element within thefilter. Q of a circuit element represents the ratio of the energy storedper cycle to the energy dissipated per cycle. The Q factor models thereal loss in each acoustic resonator, and generally more than one Qfactor may be required to describe the loss in an acoustic resonator. Qfactors may be defined as follows for the filter examples. The motionalcapacitance C_(m) may have an associated Q defined as Q_(cm)=10⁸; thestatic capacitance C₀ may have an associated Q defined as Q_(c0)=200;and motional inductance L_(m) may have an associated Q defined asQ_(Lm)=1000. (Here for simplicity the loss in the motional resonance islumped into the motional inductance and the motional capacitance isconsidered to be essentially loss-less.) Circuit designers may typicallycharacterize SAW resonators by resonant frequency ω_(R), staticcapacitance C₀, gamma γ, and Quality factor QL_(m). For commercialapplications, QL_(m) may be about 1000 for SAW resonators, and about3000 for BAW resonators.

After the circuit element values of each of the electrical circuitmodels of the respective acoustic resonators Z have been selected, theelectrical circuit model for each of the acoustic resonators Z issimulated to determine a frequency response for each of the acousticresonators Z (step 72). The simulated frequency responses of thephysical acoustic models are then respectively compared to the frequencyresponses of the electrical circuit models (step 74). If the simulatedfrequency responses of the physical acoustic models do not match thefrequency responses of the electrical circuit models (step 76), thecircuit elements of the electrical circuit models are selected at step70; for example, by modifying one of the circuit elements C₀, C_(m),L_(m), and R, and steps 72-76 are repeated again.

If the simulated frequency responses of the physical acoustic models domatch the frequency responses of the electrical circuit models (step76), the resonant frequency ω_(R), anti-resonant frequency ω_(A), andstatic capacitance C₀ of each of the electrical circuit models, and theUpper Bragg Band resonance and bulk mode loss of the initial filtercircuit design will be defined. The modeled filter circuit design isoptimized via a suitable computer optimization technique that searchesfor the combination of circuit element values that best matches thedesired filter response, i.e., the frequency response requirementsdefined in step 52 (step 78). In the illustrated embodiment, a third setof resonator characteristics is defined (e.g., by optimizing the staticcapacitance C₀ and resonant frequency ω_(R)) for each of the acousticresonators Z). Design tools, including Agilent Advanced Design System(ADS), among others, may use numerical optimization methods, such asMonte Carlo, gradient, etc., to improve the proposed filter circuitdesign. In one embodiment, one or more circuit elements in the modeledfilter circuit design can be removed during the optimization process,such as disclosed in U.S. Pat. No. 8,751,993, which has been expresslyincorporated herein by reference.

Next, the frequency response of the optimized filter circuit design iscompared to the frequency response requirements. First, each of thephysical models of the acoustic resonators Z is iteratively simulatedand modified until they match the optimized filter circuit design. Inparticular, the physical acoustic models of the acoustic resonators Zare modified; for example, by modifying a material, one or more of anumber of finger pairs, aperture size, mark-to-pitch ratio, and/ortransducer metal thickness (step 80). Then, each of the physical modelsis simulated (e.g., using a Finite Element Model (FEM)) to determine thefrequency response and a fourth set of resonator characteristics (e.g.,static capacitance C₀ and resonant frequency ω_(R)) of each of thephysical acoustic models (step 82). The fourth set of resonatorcharacteristics for each of the physical acoustic models is thenrespectively compared to the third set of resonator characteristics foreach of the acoustic resonators Z of the optimized filter circuit design(step 84). If the fourth sets of resonator characteristics of thephysical acoustic models do not match the third sets of resonatorcharacteristics of the electrical circuit models in the optimized filtercircuit design (step 86), the physical acoustic models are modified atstep 80.

If the fourth sets of resonator characteristics of the physical acousticmodels do match the third sets of resonator characteristics of theelectrical circuit models in the optimized filter circuit design (step86), the anti-resonant frequencies ω_(R), Upper Bragg Band resonances,and bulk mode losses of the physical models may not match theanti-resonant frequencies ω_(R), Upper Bragg Band resonances, and bulkmode losses of the electrical circuit models in the optimized filtercircuit design. As such, the electrical circuit models in the optimizedfilter circuit design are replaced with the frequency responses of thesimulated physical acoustic models (step 88), and the modified optimizedfilter circuit design is simulated to determine a frequency response(step 90). The simulated frequency response of the modified optimizedfilter circuit design is then compared to the frequency responserequirements defined at step 52 (step 92). If the simulated frequencyresponse does not satisfy the frequency response requirements (step 92),the process returns to step 72 whereby the electrical circuit models ofthe acoustic resonators Z are fitted to the new physical acousticmodels. If the simulated frequency response does satisfy the frequencyresponse requirements (step 92), an actual acoustic filter isconstructed based on the most recent optimized filter circuit designwith the physical resonator models (step 94). Preferably, the circuitelement values of the actual acoustic filter will match thecorresponding circuit element values in the most recent optimized filtercircuit design.

Although particular embodiments of the present invention have been shownand described, it should be understood that the above discussion is notintended to limit the present invention to these embodiments. It will beobvious to those skilled in the art that various changes andmodifications may be made without departing from the spirit and scope ofthe present invention. For example, the present invention hasapplications well beyond filters with a single input and output, andparticular embodiments of the present invention may be used to formduplexers, multiplexers, channelizers, reactive switches, etc., wherelow-loss selective circuits may be used. Thus, the present invention isintended to cover alternatives, modifications, and equivalents that mayfall within the spirit and scope of the present invention as defined bythe claims.

1. A method of designing an acoustic microwave filter in accordance withfrequency response requirements, comprising: synthesizing an initialfilter circuit model having a plurality of circuit elements comprisingan acoustic resonant element defined by an electrical circuit model;defining a physical model of the acoustic resonant element; simulatingthe physical model of the acoustic resonant element to generate a firstfrequency response; simulating the electrical circuit model of theacoustic resonant element to generate a second frequency response;comparing the first and second frequency responses; modifying at leastone parameter in the electrical circuit model of the acoustic resonatorelement based on the comparison; optimizing the initial filter circuitdesign having the modified electrical circuit model to generate anoptimized filter circuit design; comparing a frequency response of theoptimized filter circuit design to the frequency response requirements;and constructing the acoustic microwave filter from the optimized filtercircuit design based on the comparison. 2.-18. (canceled)